Question: Divide the polynomials.
Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. $\begin{array}{r} x-3 \\ x+1|\overline{x^2-2x-8} \\ \mathllap{-(}\underline{x^2+\phantom{2}x\phantom{-8}\rlap )} \\ -3x-8 \\ \mathllap{-(}\underline{-3x-3\rlap )} \\ -5 \end{array}$ We get that the quotient is $x-3$ and the remainder is $-5$, and therefore: $\dfrac{x^2-2x-8}{x+1}=x-3-\dfrac{5}{x+1}$ [I want to see a different way of performing the division.]